Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.arzx)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=2, a₃>=2

For fixed z and a₁=3/2, a₂=2, a₃=4

For fixed z and a₁=3/2, a₂=2, a₃=4, b₁=-7/2

http://functions.wolfram.com/07.27.03.arzx.01

Input Form

HypergeometricPFQ[{3/2, 2, 4}, {-(7/2), -(3/2)}, -z] == (1/(224 (1 + z)^12)) (224 + 2176 z + 16320 z^2 + 394368 z^3 + 18998560 z^4 - 355380384 z^5 + 1041342544 z^6 - 784623510 z^7 + 140893137 z^8 - 1649340 z^9 - 32340 z^10) - (6435 (1760 z^(9/2) - 13360 z^(11/2) + 23650 z^(13/2) - 11847 z^(15/2) + 1386 z^(17/2)) ArcSinh[Sqrt[z]])/(32 Sqrt[1 + z] (1 + 12 z + 66 z^2 + 220 z^3 + 495 z^4 + 792 z^5 + 924 z^6 + 792 z^7 + 495 z^8 + 220 z^9 + 66 z^10 + 12 z^11 + z^12))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]